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The Boolean expression for the circuit in the given figure is

Figure
14.27 depicts four x-t plots
for linear motion of a particle. Which of the plots represent
periodic motion? What is the period of motion (in case of periodic
motion)?

(a)

(b)

(c)

(d)

Two plane mirrors each $14\text{m}$ long are facing each other as shown in the figure. The distance between the mirrors is $\sqrt{3}\text{m}$. A light ray is incident at the corner end of one of the mirrors at an angle of incidence ${30}^{\circ }$. How many times does the ray gets reflected before it reaches the other corner end of the either mirrors?

Calculate the number of turns per unit length in a solenoid when the charge of $4\text{C}$, flows for $2\text{minutes}$, producing a magnetic field of $25\times {10}^{-5}\text{T}$.

Given are three cylindrical buckets X, Y, Z whose circular bases are of radii 1, 2, 3 units, respectively, Initially, water is filled in these buckets up to the same height. Some water is then transferred from Z to X so that they both have the same volume of water. Some water is then transferred between X and Y so that they both have the same volume of water. If h${}_y$, h${}_z$ denote the heights of water at this stage in the buckets Y,Z, respectively, then the ratio $\frac{h_y}{h_z}$ equals.

A 2 m-long string fixed at both ends is set into vibrations in its first overtone. The wave speed on the string is $200m{s}^{-1}$ and the amplitude is 0.5 cm. (a) Find the wavelength and the frequency. (b) Write the equation giving the displacement of different points as a function of time. Choose the X-axis along the string with the origin at one end and t = 0 at the instant when the point x = 50 cm has reached its maximum displacement.

Three forces act on a body and the body stays at equilibrium. The direction of the two forces are shown in the figure. The direction of the third force to keep the body in equilibrium is (Given $F_1=F_2$)

A circular coil of $20$ turns having radius $10\text{cm}$ is placed in a uniform magnetic field of $0.2\text{T}$ normal to the plane of the coil, If a current of $5\text{A}$ passes through the coil, then the torque experienced by the coil in $\left(\text{Nm}\right)$

Fusion reaction is given by ${}_6^{12}C{+}_6^{12}C{\to }_{10}^{20}Ne{+}_2^{4}He$.
If B.E. per nucleon for ${}_6^{12}C$ is X, B.E. per nucleon for ${}_{10}^{20}Ne$ is Y and B.E. per nucleon for ${}_2^{4}He$ is Z, then Q value of reaction is

The truth table for the circuit given in the figure is :

What is the relation between refractive indices ${\mu }_1,{\mu }_2\text{and}{\mu }_3$ if the behaviour of light rays is as shown in the figure. The refractive index of medium to the left of the lens is ${\mu }_1$ , that of lens is ${\mu }_3$ and that of medium to the right of lens is ${\mu }_2$ .

An infinite wire placed along z-axis has current $i_1$ in positive z-axis. Another wire PQ placed in x-y plane along y-axis carry current $i_2$ along y-axis wire PQ is at distance a from wire carrying current $i_1$. Net force acting on wire PQ is

A metallic cylindrical vessel whose inner and outer radii are $r_1$ and $r_2$ is filled with ice at $0^{\circ }\text{C}.$ The mass of the ice in the cylinder is $m$. Circular surfaces of the cylinder are sealed completely with adiabatic walls. The vessel is kept in air and the temperature of the air is ${50}^{\circ }\text{C}.$ How long will it take for the ice to melt completely?
[Thermal conductivity of the cylinder is $K$ and its length is $l$. Latent heat of fusion is $L$].

A train starts from rest with a constant acceleration $a=2m{s}^{-2}$. After 5 s, a stone is dropped from the window of the train. If the window is at a height of 2 m from the ground, what is the magnitude of the velocity of the stone 0.2 s after it was dropped? Take $g=10m{s}^{-2}$.

A ball hanging from a support by an inextensible string of length $l$ is strucked perfectly inelastically by an identical ball of mass $m$ moving with horizontal velocity of $u=\sqrt{2gl}$. Assuming the balls execute circular motion just after collision, find the tension in the string just after collision.

Two coherent sources of different intensities send waves which interfere. The ratio of maximum intensity to the minimum intensity is $25:1$. The intensities of the sources will be in the ratio

Two masses 8 kg and 12 kg are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses, and the tension in the string when the masses are released.

For the given AC LCR circuit, at a particular frequency of the AC source, the expression for current $\left(i\right)$ as a function of time $\left(t\right)$ will be -

An electric heater emits 1000 W of thermal radiation. The coil has a surface area of 0.020 $m^2$. Assuming that the coil radiates like a blackbody, find its temperature. $\sigma =6.00\times {10}^{-8}W/m^2-K^4$.

1. -0.4

A transparent thin film of uniform thickness and refractive index $n_1=1.4$ is coated on the convex spherical surface of radius R at one of a long solid glass cylinder of refractive index $n_2=1.5,$ as shown in the figure. Rays of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at a distance $f_1$ from the film, while rays of light traversing from glass to air get focused at a distance $f_2$ from the film. Then

An isothermal surface is taken on an $xy$ plane. Find the direction along which there will be largest change in temperature.

A shell is fired from cannon with a velocity V at an angle $\theta$ with the horizontal direction. At the highest point in its path, it explodes into two pieces of equal masses. One of the pieces retraces its path to the cannon. The speed of the other piece immediately after the explosion is

A sphere of radius $R$ is in contact with a wedge. The point of contact is at a distance $\frac{R}{5}$ from the ground as shown in the figure. The wedge is moving with velocity $20\text{m/s}$ towards left, then the velocity $v$ of the sphere at this instant will be:

Number of points in $[0,2\pi ]$ where $\sin x=\cos x$ is

The work done in pulling up a block of wood weighing 2 kN for a length of 10m on a smooth plane inclined at an angle of ${15}^{\circ }$ with the horizontal is

A bird moves from point $A$ $(1,-2,3)$ to $B$ $(4,2,3)$. If the speed of the bird is $10\text{m/s}$, then the velocity vector of the bird is:

A resistor with resistance of $10\text{M}\Omega$ is connected in series with a capacitor of capacitance $1\mu \text{F}$ and a battery with e.m.f. $12\text{V}$. Before the switch is closed at time $t=0,$ the capacitor is uncharged. What fraction of the initial current remains at time, $t=46\text{s}$? $(e^{-4.6}=0.01)$

A photon of energy 8 eV is incident on a metal surface of threshold frequency $1.6\times {10}^{15}Hz$, then the maximum kinetic energy of photoelectrons emitted is $(h=6.6\times {10}^{-34}Js)$